MODELS FOR OPTIMUM THERMO-ECOLOGICAL CRITERIA OF ACTUAL THERMAL CYCLES

Transcription

1 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp MODELS FOR OPTIMUM THERMO-ECOLOGICAL CRITERIA OF ACTUAL THERMAL CYCLES by Emin ACIKKALP Department of Mechanical and Manufacturing Engineering, Engineering Faculty, ilecik University, ilecik, Turkey Original scientific paper DOI: 10.98/TSCI A In this study, the ecological optimization point of irreversible thermal cycles (refrigerator, heat pump, and power cycles) was investigated. The importance of ecological optimization is to propose a way to use fuels and energy source more efficiently because of an increasing energy need and environmental pollution. It provides this by maximizing obtained (or minimizing supplied) work and minimizing entropy generation for irreversible (actual) thermal cycles. In this research, ecological optimization was defined for all basic irreversible thermal cycles, by using the first and second laws of thermodynamics. Finally, the ecological optimization was defined in thermodynamic cycles and results were given to show the effects of the cycles' ecological optimization point, efficiency, coefficient of performance, and power output (or input), and exergy destruction. Key words: ecological optimization, irreversibility, refrigeration, heat pump, power cycles Introduction In order to decrease environmental problems occurring in the world and to meet the increasing energy need, more efficient and environment friendly cycles must be designed. Finite time thermodynamics have been widely used from the 1970's onwards in order to find the performance limits of thermal systems and detect optimum values of the system. Angulo-rown [1] on the other hand recommended ecological criteria, which are another optimization method. Ecological criteria are expressed as E W T L s for finite time Camot engines, and here T L is the cold reservoir temperature and s is the entropy production of the system. Yan [] on the other hand, recommended a more reasonable principle E W T o s); here T o is the environmental temperature. This principle enables us to obtain minimum exergy destruction and maximum power output (minimum power input for heat pump and refrigeration cycles). In the literature, many studies exist in which ecological criteria are applied [3-9]. Yan and Lin [6] evaluated heat changer surface fields for an irreversible refrigerator with three heat sources; while Huang et al. [7] did the same for a refrigerator with four heat level irreversible absorption for coefficient of performance (COP) and ecological criteria. Ecological criteria used in those areas are energy based and shown as E * Q L j C T L s. j C, T L, Q L, and s terms are Carnot COP, cold reservoir temperature, refrigeration load, and entropy production, respectively. Ust et al. [30-3] recommended a new principle, which they called ecological performance coefficient (ECOP). This principle is shown as ECOP = W/T 0 s and they examined various thermodynamic cycles us- Author's acikkalp@gmail. com, emin.acikkalp@bilecik.edu.tr

2 916 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp ing this principle. In addition to those, optimizations for many cycles including Stirling- -Ericsson heat machines, internal combustion engines, and refrigeration cycles were made [33-39]. In this study, all basic thermodynamic cycles were optimized using ecological criteria and while doing this, with an aim to choosing simple and easily applicable methods. Existing ecological optimization methods were enhanced and facilitated. Contrary to other studies, here, an internal irreversibility parameter was included in the analysis, instead of accepting it as a different parameter. Researchers are expected to design ecological systems more easily by using these methods. Thermodynamic analysis y using the first law of thermodynamics, power output in ecological function was defined as the difference between the heat entering the system and the heat thrown out ( W Q Q H L) and was generalized in the form of eq. (1); this equation contains power output and exergy destruction terms. After, eq. (1) was applied to all basic thermodynamic cycles in next two sections: E Q Q H L To (1) Design parameters: selected as evaporator temperature for irreversible Rankine cycle, condenser temperature for irreversible heat pump and refrigeration cycles, non-dimensional compression parameter for, CI, Stirling cycles and non-dimensional pressure parameter for irreversible rayton and Ericsson cycles. Recognitions made for cycles are: for irreversible Rankine, heat pump and refrigeration cycles all processes are irreversible, systems follow a continuous pattern, and heat exchangers' dimensions are limited and convection coefficients are constant, and for irreversible, CI, Stirling-Ericsson and rayton cycles all processes are irreversible, specific heats are constant and average specific heats are used, piston friction is neglected, working fluid is air, which is the ideal gas, and polytrophic coefficients are constant and an average polytrophic coefficient is identified for each cycle. Environmental temperature (T o ) is accepted as K for all cycles. An internal irreversibility parameter was defined for all cycles by using the second law of thermodynamics. The second law of thermodynamics can be expressed as: Q H QL TH,WF TL,WF 0 () In order to make this inequality an equality, a coefficient must be defined. This coefficient is an internal irreversibility parameter. With the addition of the internal irreversibility parameter, the the equality in eq. (), transforms into the form: Q Q H L I TH,WF TL,WF (3) Here I is the internal irreversibility parameter of the system and can be expressed as by using eq. (3):

3 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp QT I L H,WF (4) QT L L,WF As seen in the following sections, the function, which will be optimized, can be simplified by writing an internal irreversibility parameter, as seen in eq. (4), and among the optimum values found, only heat and heat conductivity parameters will remain. The internal irreversibility parameter is greater than one in all irreversible (actual) cycles (I > 1), while in reversible cycles it will be equal to zero (I = 0). Power generation cycles Thermodynamic analysis of irreversible Rankine cycle Recently, Rankine cycle has gained importance thanks to an increase in the search for new energy technologies and more efficient systems, because this cycle can work with organic working fluids (hydrocarbons, siloxanes or refrigerants) that enable the use of energy sources at low temperatures. In addition to this, facilities which work with a conventional Rankine cycle that uses coal as fuel are still widely used. Emissions that are sent out by these facilities to the environment and entropy production must be reduced to a minimum. In fig. 1, the T-s diagram of an irreversible Rankine cycle is seen. From the first law of thermodynamics: Figure 1. T-s diagram of irreversible Rankine cycle Q Q W H,R L,R net,r (5) Here Q H,R and Q L,R can be obtained similar to the finite time thermodynamic used in refs. [40, 41]: QH,R ( ) QL,R QH,R fer, TH,R TE,R and QL,R f C,R ( T C,R t1, R t, R T L,R ) (6) t R =t 1,R +t,r (7) Here, T H,R is the combustion temperature and T L,R : TL1,R TL,R TL,R (8) From the second law of thermodynamics: Q H,R QL,R QH,R QL,R 0 or I R (9) TE,R TC,R TE,R TC,R Here, I R is the internal irreversibility coefficient of the Rankine cycle. I R and Q H,R can be obtained, respectively, by using eqs. (4) and (5)-(9): I R f f T ( T T ) C,R E,R C,R L,R T ( T T ) E,R C,R H,R E,R (10)

4 918 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp Q H, R f 1 TC,R I R 1 TE,R ( T T ) f ( T T ) E,R H,R E,R C,R L,R C,R (11) y using eqs. (1) and (5)-(11), ER is obtained as: T ( T T )( T T ) T ( T T ER f f T ( 1 T T T T ) T C,R H,R L,R C,R 0 L,R E,R L,R H,R E, R o H,R H,R E,HR E,HR H,R HR L,R )( T T ) Here, evaporator temperature is selected as design parameter and in order to detect the optimum evaporator temperature, a derivative of the Rankine cycle according to the evaporator temperature is equalized to zero ( E R /T E,R = 0 ). The corresponding value is: (1) T op, E, R TL,RTH,R D f T ( T T ) T ( E,R L,R H,R o fc,r H,R TC,R TL,R ) ( TL,R To ) T H,RTo f E,RTL,R ( TH,R To ) (13) D ( T f T K T f ) (14) H,R E,R L,R C,R C,R C,R ( T f T f T f T f ) (15) C,R C,R L,R C,R L,R C,R L,R E,R Thermodynamic analysis of irreversible and CI cycles Internal combustion engines are the most widely used power cycles. When the emissions released by these cycles are taken into consideration, they have serious negative effects on the environment. Although it is estimated that fossil fuels will deplete soon, it can be said that internal combustible engines could be used in power production, by considering the studies that are carried out on fuels which can be produced in a laboratory. If we take into account the harmful effects on the environment and relatively low efficiencies, the importance of designing internal combustible engines in an environmental friendly way becomes apparent. In this section, and CI engines were optimized by taking ecological criteria into consideration. Figure show the T-s diagram of analyzed engines. Irreversible engine From the first law of thermodynamics: Figure. T-s diagram of irreversible, CI, and rayton Q Q W cycles [4, 43] H, L, net, (16)

5 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp m k ( ), m K QH, T3, T, QL, 1 k 1 k For engine: ( T T ) (17) 4, 1, V1, V4, T, T3, T, e, x, x ( e) n 1 3, a, V, V3, T1, T4, T1, T3, cv,-3, T, T1, x, T4,, K cv,, -3 cv,, 4-1, k x cv,4-1, (18) From the second law of thermodynamics: Q H, QL, QH, QL, 0 or I T3, T1, T3, T1, (19) Here, I is the internal irreversibility coefficient of engine. I and Q L, can be obtained as follows by using eqs. (4) and (16)-(19): I a k x (0) Q L, y using eqs. (1) and eqs. (16)-(1), E E m kt1, ( a x ) 1+ k is obtained as: m K ( a x )[ kt x a ( kt, x T, a x ( 1 k ) o T )] Here, in order to detect optimum compression rate, a derivative of the engine according to the compression rate of its ecological function is equalized to zero (E /x = 0). The corresponding value is: xop, a ( T T 1, o ) k ( at1, To ) (3) Irreversible CI engine From the first law of thermodynamics: Q Q W (4) m K k QH,CI 1 kci For CI engine: CI CI CI H,CI L,CI net,ci ( T T ), Q 3, CI, CI L,CI m CI K 1 k CI CI (1) () ( T4, CI T1, CI ) (5) V1, CI T, CI T4, CI wci T CI e CI, xci,, xci, ( e ) n CI 1 3 CI, aci, V, CI T1, CI T3, CI xci T1, CI T3, CI wci c T, CI T1, CI xci, T4, CI, w 1 CI rnci,,, KCI cp, -3, CI cv, 4-1, CI, kci xci c,, From the second law of thermodynamics: Q H,CI QL,CI QH,CI QL,CI 0 or ICI T T T T 3, CI 1, CI 3, CI 1,CI p-3ci v4-1ci (6) (7)

6 90 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp Here, I CI is the internal irreversibility coefficient of CI engine. I CI and Q L,CI can be obtained by using eqs. (4) and (4)-(7), respectively: E CI I CI aci ( aci wci xci ) k x ( a x ) CI CI CI CI m CI KCIT1, CI ( aci wci xci ) QLCI, kci ( 1 kci ) xci y using eqs. (1) and (4)-(9), ECI is obtained as: KCI mci { aci xci ( T, CI To kcito kcit, CI ) a [ w CI a x ( 1 k ) 1 1 CI o 1 CI CI CI o CI CI CI CI T T, ][ w k T x )]} Here, in order to detect the optimum compression rate, a derivative of CI engine according to the compression rate of its ecological function is equalized to zero ( E CI / x CI = 0). The corresponding value is: a ( T T w CI 1, CI o ) CI xop,ci (31) k ( a T T ) CI CI 1, CI o Thermodynamic analysis of irreversible rayton cycles Since the rayton cycle generates an ideal model for continuous combustion gas turbines, it has an important place in thermodynamic optimization studies. There are various studies examining parameters such as maximum power, maximum power density, and thermal efficiency of the rayton cycle under finite time, finite area, and finite rate restrictions and which determine its performance limits [44-55]. Figure shows the T-s diagram of the irreversible rayton cycle. From the first law of thermodynamics: Q Q W (3) Q H, For rayton cycles: H, L, net, (8) (9) (30) mkk ( ), mk T3, T, QL, ( T4, T 1, ) (33) 1 k 1 k P, P3, T, T3, T v, x, x ( n) n 3,, a, V1, P4, T1, T4, T1, T3, cp-3,, T, T1, x, T4,, K cp, -3, cp, 4-1,, k (34) x cp4-1,, From the second law of thermodynamics: Q H, QL, QH, QL, 0 or I (35) T T T T ( n 1) 3, 1, 3, CI 1, Here, I is the internal irreversibility coefficient of the rayton cycle. I and Q L, can be obtained by using eqs. (4) and (3)-(35), respectively:

7 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp mkt ( a x) QL, 1 k y using eqs. (1) and (3)-(37), E is obtained as: E I a (36) k x mk ( a x)[ ktx o a( kx )] a x (1 + k ) Here, in order to detect optimum pressure rate, a derivative of the rayton cycle according to the compression rate of its ecological function is equalized to zero (E /x = 0). The corresponding value is: xop, a (39) k ( a 1) Thermodynamic analysis of irreversible Stirling and Ericsson cycles Ericsson and Stirling engines have attracted the attention of several generations of engineers and physicists due to their theoretical potential to provide high conversion efficiency that approached those of the Carnot cycle. However, use of these engines did not prove to be successful due to relatively poor material technologies available at that time. As, the world community has become much more environmentally conscious, further attention in these engines has been again received because these engines are inherently clean and thermally more efficient. Moreover, as a result of advances in material technology, these engines are currently being considered for variety of applications due to their many advantages like low noise, less pollution and their flexibility as an external combustion engine to utilize a variety of energy sources or fuels. These engines are also under research and development for their use as heat pumps, replacing systems that are not ecological friendly and environmentally acceptable. Nowadays, the popularity of these engines is growing rapidly due to their many advantages like being more efficient, less pollution levels and their flexibility as external combustion engines to utilize different energy sources such as solar energy. The central receiver and parabolic dish solar systems based Stirling/Ericsson heat engine is more efficient and suitable for both the terrestrial [33, 56] and non-terrestrial [57, 58] solar installations. In the literature, Erbay and Yavuz [59-6], investigated irreversible Stirling and Ericsson engines. In this study their model was adopted for the analyzing of the Stirling-Ericsson engines (fig. 3). From the first law of thermodynamics: Q Q W (40) H,SE L,SE net,se Figure 3. T-s diagram of irreversible Stirling-Ericsson cycle [3-35] (37) (38)

8 9 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp l n ( ) 1 l n QH,SE mset4, SE R 1 xser QL m SET, SEr R 1 ( 1n )( l 1 ) x SEr ( 1 n)( l 1 ) ner 1 ner V x n S S SE S, ( e ) P, Er, es, ner, ner V, S P1,Er T4, SEr T, SEr aser, T1, SEr, T3, SE T4, SEr xser, T, SEr xser q l n TH1, SEr TH SEr TH, SEr ( 1n)( l 1), SEr, TL1, SEr TL, SEr, TLSEr, as defined in [30-33]. From the second law of thermodynamics: Q H,SEr QL,SEr QH,SEr QL,SEr 0 or I SEr (43) T T T T 4 4 (41) (4) Here, I SEr is the internal irreversibility coefficient of Stirling and Ericsson cycles. I SEr can be obtained by using eqs. (4) and (40)-(43), respectively: and Q L,SEr I SEr 1 xser (44) 1 x Q m SEr L,SEr aser qser SEr RT, SErTL,SEr TH,SEr x SEr (45) y using eqs. (1) and (40)-(45), ESEr is obtained as: E a q m RT SEr SEr SEr SEr, SEr ( TL,SEr To TH,SEr xser Tox TH,SEr xser SEr )( 1 xser ) (46) Here, in order to detect an optimum pressure rate for the Ericsson cycle or an optimum compression rate for the Stirling cycle, a derivative of cycle of Stirling-Ericsson cycles according to the compression of their ecological function is equalized to zero (E SEr /x SEr = 0 ). The corresponding value is: TL,SEr To xop, SEr (47) T T H,SEr o Figure 4. T-s diagram of irreversible heat pump and refrigerators cycles Heat pump and refrigeration cycles Heat pump and refrigeration cycles work with the same cycle requiring power from the environment. Cycles which are more efficient and harm the environment less must be designed by reducing the power obtained from the environment and entropy production. In this section, limits of these cycles were determined by using ecological criteria. Figure 4 shows the T-s diagram of irreversible heat pump and refrigerator cycles.

9 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp Thermodynamic analysis of general irreversible heat pump and irreversible refrigerator systems From the first law of thermodynamics, power input (exergy input) for heat pump and refrigeration cycles is equal to the difference between the heat entering the system and the heat leaving the system. This expression can be obtained as follows: Q Q W H, hr L, hr net, hr (48) Here, Q H,R and Q L,R can be obtained, similar to the finite time thermodynamic used in references [40-41]: QH, hr Q ( T T ) Q QL, hr H, hr fc, hr H, hr E, hr and L, hr f E, hr ( TC, hr TL, hr ) (49) t t 1, hr, hr t hr =t 1,hr +t,hr (50) Here, T H,hr and T L,hr are: TH1, hr TH, hr TL1, hr TL, hr TH, hr, TL, hr (51) From the second law of thermodynamics: Q H, hr QL, hr QH, hr QL, hr 0 or I H, hr (5) TE, hr TC, hr TE, hr T C, hr Here, I hr is the internal irreversible coefficient of heat pump and refrigeration cycles. I hr and Q H, hr can be obtained by using eqs. (4) and (49)-(5), respectively: Q H, hr I hr f f T ( T T ) C, hr E, hr C, hr H, hr T ( T T ) E, hr C, hr L, hr E, hr 1 TE, hr T 1 C, hr ( TC, hr TH, hr ) fc, hr I hr fe, hr ( T L, hr T E, hr ) y using eqs. (1) and (50)-(55), E hr is obtained as: (53) (54) E hr fe, hrth, hr ( TE, hr TL, hr )( TL, hr To ) fc, hrtl, hr ( TC, hr TH, hr )( TH, hr To ) T T T T T H, hr (1 C, hr C, hr H, hr )T H,r L, hr Here, condenser temperature is selected as design parameter and in order to detect optimum condenser temperature, the derivative of the heat pump refrigerator cycle according to condenser temperature is equalized to zero ( E hr / T C,hr = 0). The corresponding value is: T op,c, hr TL, hrth, hr J 1 T ( TH, hr To ) T ( T hr H, hr E, hr TL, hr ) ( TL, hr To ) T ( T T ) fc, hr L, hr T f H, hrto J E, f C, hr L,hr H,Hhr o (55) (56)

10 94 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp Results and numerical examples J T f T f f T (57) 1 L, hr E, hr H, hr C, hr E, hr E, hr J T f T f T f (58) E, hr E, hr L, hr C, hr L, hr E, hr In this section, optimum points for all basic thermodynamic cycles were determined and they were discussed in detail for each cycle separately. Numerical examples were selected in a way that would be close to the values met in practice and by using references [3-9, 56-6]. Figure 6. Effect of e on the E, W, and ExD for irreversible engine Irreversible Rankine cycle For numerical calculations, the working parameters of Rankine cycle are: T H,R = 1000 K, T C,R = 350 K, T L,R = 300 K, f E,R = 15 kw/k, and f C,R = 0.5 kw/k. Figure 5 shows the variation of power output ( W), thermal efficiency (h), ecological function ( E), exergy destruction (ExD), and the internal irreversibility parameter (I) of the Rankine cycle with regard to evaporator temperature. Evaporator temperature for the Rankine cycle was detected as K. It is seen that with the increase of evaporator temperature, ecological function rises up to the optimum evaporator temperature, while power output and thermal efficiency decrease as ExD increase. The reason for the decrease in power and efficiency is the increase of irreversibility and exergy destruction. y examining eqs. (6) and (10), it can be clearly seen that internal irreversibility Figure 5. Effect off T E on E, W, I, ExD, and h for and entropy production (exergy destruction) will increase with the increase of irreversible Rankine cycle evaporator temperature. Irreversible engines For numerical calculations, the working parameters of the engine are: T 1, = 350 K, a =4, m = 0.5 kg/s, c vs,i,-3 = 0.8 kj / kgk, n = Figures 6 and 7 show the variation of power output ( W), thermal efficiency (h), ecological function ( E), exergy destruction (ExD), and the internal irreversibility parameter (I) of the engine with regard to compression rate. The optimum compression rate for the engine was detected as 1.5. It is seen that with the increase of the compression rate, ecological function rises up to the optimum compression rate, then starts to decrease and thermal efficiency increases, while power output, ExD, and the internal irreversibility parameter decrease. The reason for the decrease in power and irreversibility parameter can be

11 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp seen by looking at eqs. (0)-(). The decrease of ExD and the direct irreversibility parameter are directly proportional since entropy production is the result of irreversibilities. Irreversible CI engines For numerical calculations, the working parameters of the CI engine are: T 1,CI = 350 K, a =6, m = 0.5 kg/s, k CI = 1.1, K CI = 1.4 kj/kgk, w CI = 1.3, and n CI = Figures 8 and 9 show the variation of power output ( W), thermal efficiency (h), ecological function ( E), energy destruction (ExD) and the internal irreversibility parameter (I) of the CI engine with regard to compression rate. The optimum compression rate for the CI engine was detected as It is seen that with the increase of compression rate, ecological function rises up to the optimum compression rate, then starts to decrease and thermal efficiency increases, while power output, exergy destruction and the internal irreversibility parameter decrease. The reason for the decrease in power and irreversibility parameter can be seen by looking at eqs. (8)-(30). A decrease of exergy destruction and the direct irreversibility parameter are directly proportional since entropy production is the result of irreversibilities. Figure 7. Effect of e on the h and I for irreversible engine Figure 8. Effect of e on the E, W, and ExD for irreversible CI engine Irreversible rayton cycles For numerical calculations, the working parameters of the rayton cycle are: T 1, = 300 K, a = 3.5, m = 0.5 kg/s, c p,,-3 = 1.1 kj/kgk, and n = Figures 10 and 11 show the variation of power output ( W), thermal efficiency (h), ecological function ( E), exergy destruction (ExD), and the internal irreversibility parameter (I) of the rayton cycle with regard to pressure rate. The optimum pressure rate of the rayton cycle was detected as 5.1. It is seen that with the increase of pressure rate, ecological function rises up to the optimum pressure rate, then Figure 9. Effect of e on the h and I for irreversible CI engine starts to decrease and thermal efficiency increases, while power output, exergy destruction and the internal irreversibility parameter decrease. The reason for the decrease in power and irreversibility parameter can be seen by looking at eqs. (36)-(38). A decrease of exergy destruction and direct irreversibility parameter are directly proportional since entropy production is the result of irreversibilities.

12 96 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp Figure 10. Effect of n on E, W, and ExD for irreversible rayton cycle Figure 11. Effect of n on h and I for irreversible rayton cycle Irreversible Stirling-Ericsson engine For numerical calculations, the working parameters of the Stirling-Ericsson cycle are: T 1,SEr = 350 K, a SEr =3, m s = 0.5 kg/s, q = 5.34, R = 0.87 kj/kgk, T H,SEr = 1000 K, and T L,SEr = = 300 K. Figures 1 and 13 show the variation of power output ( W), thermal efficiency (h), ecological function ( E), exergy destruction (ExD) and the internal irreversibility parameter (I) of Stirling-Ericsson cycle with regard to compression rate. The optimum compression and pressure rates of the Stirling-Ericsson cycle were detected as.49. It is seen that with the increase of pressure and compression rates, ecological function rises up to the optimum compression rate, then starts to decrease and thermal efficiency increases, power output, and exergy destruction increase, while in contrast, thermal efficiency and the internal irreversibility parameter decrease. The reason for the increase in power and decrease in irreversibility parameter can be seen by looking at eqs. (44)-(46). Figure 1. Effect of e on E, h, I, W, and ExD for irreversible Sitirling engine Figure 13. Effect of n on E, h, I, W, and ExD for irreversible Ericsson engine Irreversible heat pump and refrigeration cycles For numerical calculations, the working parameters of the heat pump and refrigeration cycle are: T H,hr = 300 K, T E,hr = 50 K, T L,hr = 60 K, f E,hr = 0.1 kw/k, and f C,hr = 8 kw/k. Figures 14 and 15 show the variation of power output ( W), thermal efficiency (h), ecological func-

13 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp Figure 14. Effect of T C on Q H (heating load), W, I, E, ExD, and COP for irreversible heat pump cycle Figure 15. Effect of T C on Q L (cooling load), W, I, E, ExD, and COP for irreversible refrigerator tion ( E), exergy destruction (ExD) and the internal irreversibility parameter (I) of heat pump and refrigeration cycles with regard to condenser temperature. The optimum condenser temperature for the heat pump and refrigeration cycle was detected as K. With the increase in condenser temperature ExD, heat load in the heat pump cycle and refrigeration load in the refrigeration cycle dramatically increased until reaching a value of 301 K and started to decrease after that value, while the COP value dramatically decreased until reaching 301 K and decreasing speed dropped after this value. Ecological function on the other hand decreases regularly after the optimum condenser temperature. Conclusions In this study, ecological optimization was made for all basic thermodynamic irreversible cycles and the results were discussed. All cycles were evaluated by taking exergy destruction, thermal efficiency, COP, power output or power input, and internal irreversibility parameters into account. y regarding the results presented within the scope of this study, the actual thermodynamic cycles to be used were aimed to be designed with the least exergy destruction and as environmental friendly as possible. Nomenclature c p specific heat, [kjkg 1 K] COP coefficient of performance E ecological funcion ExD exergy destruction [kw] I internal irreversibility parameter K sum of specific heats, [kjkg 1 K] k ratio of specific heats m mass flow, [kgs 1 ] n polytrophic coefficient R ideal gas constant, [kjkg 1 K] r cut-off ratio T temperature, [kw] t time, [s] Q heat, [kj] Q heat, [kw] W work, [kw] WF working fluid w dimensionless compression ratio parameter x dimensionless compression ratio or dimensionless pressure ratio parameter Greek symbols a ratio of the highest and the lowest temperature of the cycle e compression ratio h efficiency q a coefficient for Ericsson and Stirling engines l isentropic coefficient n pressure ratio s entropy generation, [kwk 1 ] f heat conductance, [kwk 1 ] Subscripts C rayton condenser

14 98 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp CI E H hr L R compression injection engine evaporator high heat pump or refrigeration low Rankine r S SEr o op refrigerator Stirling Stirling or Ericsson engine spark injection engine environmental conditions optimum References [1] Angulo-rown, F., An Ecological Optimization Criterion for Finite-Time Heat Engines, Journal of Applied Physic, 69 (1991), 11, pp [] Yan, Z., Comment on Ecological Optimization Criterion for Finite-Time Heat-Engines, Journal of Applied Physic, 73 (1993), 7, pp [3] Chen, L., et al., Power, Efficiency, Entropy-Generation Rate and Ecological Optimization for a Class of Generalized Irreversible Universal Heat Engine Cycles, Applied Energy, 84 (007), 5, pp [4] Chen, L., et al., Ecological Optimization for Generalized Irreversible Carnot Engines, Applied Energy, 77 (004), 3, pp [5] Chen, L., et al., Exergy-ased Ecological Optimization for a Generalized Irreversible Carnot Heat-Pump, Applied Energy, 84 (007), 3, pp [6] Yan, Z., Lin, G., Ecological Optimization Criterion for an Irreversible Three-Heat-Source Refrigerator, Applied Energy, 66 (000), 3, pp [7] Huang, Y., et al., Performance Optimization for an Irreversible Four-Temperature-Level Absorption Heat Pump, International Journal of Thermal Science, 4 (008), 4, pp [8] Cheng, C., Chen, C., The Ecological Optimization of an Irreversible Carnot Heat-Engine, J. Phys. D: Appl. Phys., 30 (1997), 11, pp [9] Xia, D., et al., Universal Ecological Performance for Endoreversible Heat Engine Cycles, Int. J. Ambient Energy, 7 (001), 1, pp [10] Zhang, W., et al., Exergy-ased Ecological Optimal Performance for a Universal Endoreversible Thermodynamic Cycle, Int. J. Ambient Energy, 8 (007), 1, pp [11] Chen, L., et al., Exergy-ased Ecological Optimization of Linear Phenomenological Heat Transfer Law Irreversible Carnot Engines, Applied Energy, 83 (006), 6, pp [1] Zhu, X., et al., The Ecological Optimization of a Generalized Irreversible Carnot Engine with a Generalized Heat-Transfer Law, Int. J. Ambient Energy, 4 (003), 4, pp [13] Zhu, X., et al., Effect of Heat Transfer Law on the Ecological Optimization of a Generalized Irreversible Carnot Engine, Open Sys. Inf. Dyn., 1 (005), 3, pp [14] Li, J., et al., Ecological Performance of an Endoreversible Carnot Heat Engine with Complex Heat Transfer Law, Int. J. Sustainable Energy, 30 (011), 1, pp [15] Li, J., et al., Ecological Performance of a Generalized Irreversible Carnot Heat Engine with Complex Heat Transfer Law, Int. J. Energy and Environment, (011), 1, pp [16] Tu, Y., et al., Exergy-ased Ecological Optimization for an Endoreversible rayton Refrigeration Cycle, Int. J. Exergy, 3 (006),, pp [17] Chen, L., et al., Ecological Optimization for Generalized Irreversible Carnot Refrigerators, J. Phys. D: Appl. Phys., 38 (005), 1, pp [18] Zhu,X.,et al., Exergy ased Ecological Optimization for a Generalized Irreversible Carnot Refrigerator, J. Energy Institute, 79 (006), 1, pp [19] Chen, L., et al., Ecological Optimization of a Generalized Irreversible Carnot Refrigerator for a Generalized Heat Transfer Law, Int. J. Ambient Energy, 8 (007), 4, pp [0] Li, J., et al., Ecological Performance of an Endoreversible Carnot Refrigerator with Complex Heat Transfer Law, Int. J. Ambient Energy, 3 (011), 1, pp [1] Chen, L., et al., Ecological Optimization of a Generalized Irreversible Carnot Refrigerator in Case of Q(DT n ) m, Int. J. Sustainable Energy, 31 (01), 1, pp [] Tyagi, S. K., et al., Ecological Optimization and Parametric Study of Irreversible Stirling and Ericsson Heat Pumps, J. Phys. D: Appl. Phys., 35 (00), 16, pp [3] Zhu, X., et al., Effect of Heat Transfer Law on the Ecological Optimization of a Generalized Irreversible Carnot Heat Pump, Int. J. Exergy, (005), 4, pp [4] Zhu,X.,et al., The Ecological Optimization of a Generalized Irreversible Carnot Heat Pump for a Generalized Heat Transfer Law, J. Energy Institute, 78 (005), 1, pp. 5-10

15 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp [5] Chen, L., et al., Effect of a Complex Generalized Heat Transfer Law on Ecological Performance of an Endoreversible Carnot Heat Pump, Int. J. Ambient Energy, 30 (009),, pp [6] Li, J., et al., Optimal Ecological Performance of a Generalized Irreversible Carnot Heat Pump with a Generalized Heat Transfer Law, Termotehnica, 13 (009),, pp [7] Liu, X., et al., Ecological Optimization of an Irreversible Harmonic Oscillators Carnot Heat Engine, Science in China Series G: Physics, Mechanics & Astronomy, 5 (009), 1, pp [8] Wang, W., et al., Optimal Heat Conductance Distribution and Optimal Intercooling Pressure Ratio for Power Optimization of an Irreversible Closed Intercooled Regenerated rayton Cycle, Journal of Energy Institute, 79 (006),, pp [9] Wang, W., et al., Ecological Optimization of an Irreversible ICR Gas Turbine Cycle, Int. J. Exergy, 9 (011), 1, pp [30] Ust, Y., et al., Performance Analysis and Optimization of an Irreversible Dual-Cycle ased on an Ecological Coefficient of Performance Criterion, Applied Energy, 8 (005), 1, pp [31] Ust, Y., Sahim,., Performance Optimization of Irreversible Refrigerators ased on a New Thermo-Ecological Criterion, International Journal of Refrigeration, 30 (007), 3, pp [3] Ust, Y., et al., Ecological Coefficient of Performance Analysis and Optimization of an Irreversible Regenerative rayton Heat Engine, Applied Energy, 83 (006), 6, pp [33] Tyagi, S. K., et al., Ecological Optimization and Performance Study of Irreversible Stirling and Ericsson Heat Engines, J. Phys. D: Appl. Phys., 35 (00), 0, pp [34] Sahin,., et al., A Comparative Performance Analysis of Endoreversible Dual Cycle under Maximum Ecological Function and Maximum Power Conditions, Exergy, an International Journal, (00), 3, pp [35] Zhu, X., et al., Exergy-ased Ecological Optimization for a Generalized Carnot Refrigerator, Journal of Energy Institute, 79 (006 ), 1, pp [36] Chen, L., et al., Optimal Temperatures and Maximum Power Output of a Complex System with Linear Phenomenological Heat Transfer Law, Thermal Science, 13 (009), 4, pp [37] Ge, Y., et al., Optimal Paths of Piston Motion of Irreversible Diesel Cycle for Minimum Entropy Generation, Thermal Science, 15 (011), 4, pp [38] Wu, F., et al., Work Output and Efficiency of a Reversible Quantum Otto Cycle, Thermal Science, 14 (010), 4, pp [39] Ge, Y., et al., Finite Time Thermodynamic Modeling and Analysis for an Irreversible Atkinson Cycle, Thermal Science, 14 (010), 4, pp [40] Chen, J., The Maximum Power Output and Maximum Efficiency of an Irreversible Carnot Heat Engine, J. Phys. D: Appl. Phys, 7 (1994), 6, pp [41] Aragon-Gonzales, G., et al., A Criterion to Maximize the Irreversible Efficiency in Heat Engines, J. Phys. D: Appl. Phys, 36 (003), 3, pp [4] Wu, C., et al., Ecological Optimization Performance of an Irreversible Quantum Engine Powering with an Ideal Fermi Gas, Open Sys. & Information Dynamic, 13 (006), 1, pp [43] aierlein, R., Thermal Physics, ISN , Cambridge, UK, 1999 [44] Sogut, S. S., et al., The Effects of Intercooling and Regeneration on Thermo-Ecological Performance Analysis of an Irreversible-Closed rayton Heat Engine with Variable-Temperature Thermal Reservoirs, J. Phys. D: Appl. Phys., 39 (006), 1, pp [45] Wu, C., Kiang, R. L.,Work and Power Optimization of a Finite-Time rayton Cycle, Int. J. Ambient Energy, 11 (1990), 3, pp [46] Wu, C., Kiang, R. L., Power Performance of a Nonisentropic rayton Cycle, ASME J. Eng. Gas Turbines Power, 113 (1991), 4, pp [47] Sahin,., et al., Efficiency of a Joule-rayton Engine at Maximum Power Density, J. Phys. D: Appl. Phys., 8 (1995), 7, pp [48] Sahin,., et al., Maximum Power Density Analysis of an Irreversible Joule-rayton Engine, J. Phys. D: Appl. Phys., 9 (1996), 5, pp [49] Sahin,., et al., A Comparative Performance Analysis of Irreversible Regenerative Reheating Joule-rayton Engines Under Maximum Power Density and Maximum Power Conditions, J. Phys. D: Appl. Phys., 31 (1998), 17, pp [50] Cheng, C. Y., Chen, C. K., Power Optimization of an Irreversible rayton Heat Engine, Energy Sources, 1 (1997), 5, pp

16 930 THERMAL SCIENCE: Year 013, Vol. 17, No. 3, pp [51] Cheng, C. Y., Chen, C. K., Power Optimization of an Endoreversible Regenerative rayton Cycle, Energy, (1996), 4, pp [5] Chen, L., et al., Theoretical Analysis of the Performance of a Regenerative Closed rayton Cycle with Internal Irreversibilities, Energy Convers. Manage., 3 (1997), 9, pp [53] Roco,J.M.M.,et al., Optimum Performance of a Regenerative rayton Thermal Cycle, J. Appl. Phys., 8 (1997), 6, pp [54] Chen, L., et al., Power Density Analysis and Optimization of a Regenerated Closed Variable-Temperature Heat Reservoir rayton Cycle, J. Phys. D: Appl. Phys., 3 (001), 6, pp [55] Chen, L., et al., Performance Comparison of an Endoreversible Closed Variable Temperature Heat Reservoir rayton Cycle under Maximum Power Density and Maximum Power Conditions, Energy Conv. Managt., 4 (00), 1, pp [56] lank, D. A., Wu, C., Power Limit of an Endoreversible Ericsson Cycle with Regeneration, Energy Conv. Mangt., 37 (1996), 1, pp [57] Chen, J., et al., Efficiency ound of a Solar-Driven Stirling Heat Engine System, Int. J. Energy Res., (1998), 9, pp [58] lank, D. A., Wu, C., Finite Time Power Limit for Solar-Radiant Ericsson Engines for Space Applications Appl. Thermal Eng., 18 (1996), 1, pp [59] Erbay,., Yavuz, H., The Maximum Cooling Density of a Realistic Stirling Refrigerator, J. Phys. D: Appl. Phys., 31 (1998), 3, pp [60] Erbay,., Yavuz, H., Analysis of Stirling Heat Engine at Maximum Power Conditions, Energy, (1997), 7, pp [61] Erbay, L.., Yavuz, H., Analysis of an Irreversible Ericsson Engine with a Realistic Regenerator, Applied Energy, 6 (1999), 3, pp [6] Erbay, L.., Yavuz, H., Optimization of the Irreversible Stirling Heat Engine, Int. J. Energy Res., 3 (1999), 10, pp Paper submitted: September 18, 011 Paper revised: May 1, 01 Paper accepted: May 6, 01